an introduction to energy-economic computable general

An introduction to energy-economic computable general equilibrium model

Niven [email protected]

EPPA WorkshopSunday River, Newry, ME

http://globalchange.mit.edu/

Supplementary notes:

An illustrative energy-economic computable general equilibrium model

1. A simple energy-economic model (ENERGY1.gms)

2. An energy model with emissions and a cap-and-trade policy (ENERGY2.gms)

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Overview

• ENERGY1.gms identifies five energy sectors (coal, crude oil, refined oil, gas and electricity) and groups other sectors in a single sector (CO2

emissions are not considered at this stage)

SET i Sectors /

cru Crude oil

oil Refined oil

col Coal

gas Gas

ele Electricity

oth Other output/;

SET f Factors of production /

lab Labor

cap Capital

res Natural resources /;

ALIAS (i,j);

SET ele(i) Electricity /ele/;

SET ff(i) Fossil fuels /cru,col,gas/;

SET fe(i) Final energy /oil,col,gas/;

SET en(i) Energy markets /gas,ele,oil,col,cru/;

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A simple energy-economic model (ENERGY1.gms)

Subsets to assist model specification

• Data for the model is sourced from edata.gms

$include edata.gms

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Input/output Sector

Gas Electricity Oil Coal Crude Oil OTHR HH

Gas 150 -60 -70 -20

Electricity 850 -750 -100

Oil -30 500 -460 -10

Coal -35 50 -10 -5

Crude Oil -300 300

OTHR -65 -325 -175 -15 -170 24790 -24040

Capital -50 -300 -15 -10 -70 -9500 9945

Labor -20 -100 -10 -10 -10 -14000 14150

Gas resource -15 15

Coal resource -15 15

Crude oil resource -50 50

• Variable assignments in ENERGY1

$SECTORS:

W ! Welfare index

Y(i)$vom(i) ! Output index

$COMMODITIES:

PW ! Welfare price index

PY(i)$vom(i) ! Output price index

PL ! Labor price index

PK ! Capital price index

PR(i)$vfm("res",i) ! Natural resources price index

$CONSUMERS:

HH ! Representative household

• Production in each sectors is a multi-level next of constant elasticity of substitution functions

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* Fossil fuel production (crude oil, coal, gas)

$PROD:Y(ff)$vom(ff) s:sigma("res_oth") b:0 va(b):sigma("k_l")

O:PY(ff) Q:vom(ff)

I:PY(j) Q:vfi(j,ff) b: a:HH T:tf(j,ff)

I:PL Q:vfm("lab",ff) va:

I:PK Q:vfm("cap",ff) va:

I:PR(ff) Q:vfm("res",ff)

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The ‘b’ nest is a sub-nest of ‘s’ by default ‘va’ is assigned as a sub-nest of ‘b’

Nesting assignments – unless

otherwise noted, each input is assigned to the top level (s)

nest

* Consumer welfare function

$PROD:W s:sigma("top_fd") e:sigma("ene_fd")

O:PW Q:vthp

I:PY(i)$(not fe(i)) Q:vhp(i) e:$ele(i)

I:PY(fe) Q:vhp(fe) e:

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$PROD:W s:sigma("top_fd") e:sigma("ene_fd")

O:PW Q:vthp


I:PY(fe) Q:vhp(fe) e:

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* Electricity production

$PROD:Y(i)$(vom(i) and ele(i)) s:0 kle:sigma("e_kl") va(kle):sigma("k_l")

+ ene(kle):sigma("fe")

O:PY(i) Q:vom(i)

I:PY(j)$(not fe(j)) Q:vfi(j,i) a:HH T:tf(j,i)

I:PL Q:vfm("lab",i) va:

I:PK Q:vfm("cap",i) va:

I:PY(fe) Q:vfi(fe,i) ene: a:HH T:tf(fe,i)

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* Other output and refined oil production

$PROD:Y(i)$(vom(i) and not ele(i) and not ff(i)) s:0 kle(s):sigma("e_kl")

+ va(kle):sigma("k_l") e(kle):sigma("ele_fe") ne(e):sigma("fe")

O:PY(i) Q:vom(i)

I:PY(j)$(not fe(j)) Q:vfi(j,i) e:$ele(j) a:HH T:tf(j,i)



I:PY(fe) Q:vfi(fe,i) ne: a:HH T:tf(fe,i)

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• ENERGY1 implements a 50% tax on coal used as an intermediate input and reports changes in output and welfare.

tf("col",i) = 0.5;

$include ENERGY1.gen

solve ENERGY1 using mcp;

PARAMETER

OUTPUT(*,i) Output

WELFARE(*) Welfare;

OUTPUT("BASE",i) = vom(i);

OUTPUT("SIM",i) = vom(i)*Y.L(i);

OUTPUT("%C",i) = 100*(OUTPUT("SIM",i) - vom(i))/vom(i);

WELFARE("%C") = 100*(W.L - 1);

DISPLAY OUTPUT, WELFARE;

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• When operating large-scale models, sending output to a gdx file allows the user to view variable and parameter values and definitions (if included) easily. ENERGY1 sends all model output to ENERGY1_OUTPUT.gdx.

EXECUTE_UNLOAD "ENERGY1_OUTPUT.gdx“

Exercises

1. Implement a 50% tax on coal used for electricity production without taxes on coal elsewhere.

2. When there is a 50% tax on coal used in all sectors, change the value of sigma("fe") from 1.2 to 2 and interpret the results.

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• ENERGY2 adds CO2 emissions from fossil fuels to ENERGY1 and considers a cap-and-trade policy

• The level of the cap is represented by the parameter clim and an emissions price declaration is included under the $COMMODITIES command

PARAMETER

fico2(j,i) CO2 emission by fuel for each sector - million

metric tons

hhco2(i) CO2 emissions from household consumption by fuel

type - million metric tons

clim CO2 emissions limit;

clim = 0;

$COMMODITIES:

PCO2$clim ! Price of co2 emissions

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An energy model with emissions (ENERGY2.gms)

Setting clim = 0 turns off the carbon constraint

(to replicate the benchmark equilibrium)

• Emissions are introduced by applying fixed carbon coefficients per unit of energy from oil, coal and gas

• Producers and households are required to purchase an emissions allowance for each ton of CO2 emissions


$PROD:W s:sigma("top_fd") e:sigma("ene_fd") oil(e):0 col(e):0 gas(e):0

O:PW Q:vthp


I:PY(“oil”) Q:vhp(“oil”) oil:

I:PCO2$clim Q:hhco2(“oil”) P:1e-5 oil:

I:PY(“col”) Q:vhp(“col”) col:

I:PCO2$clim Q:hhco2(“col”) P:1e-5 col:

I:PY(“gas”) Q:vhp(“gas”) gas:

I:PCO2$clim Q:hhco2(“gas”) P:1e-5 gas:

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Oil and CO2 allowances are included in a

‘Leontief’ (fixed proportions) nest

No emissions price in the base data and a CES function

calibrated to a commodity with a zero cost share will always be zero, so the “P:” field is used to assign a

“small” positive price

• A more succinct but equivalent representation of the consumer welfare function


$PROD:W s:sigma("top_fd") e:sigma("ene_fd") oil(e):0 col(e):0 gas(e):0

O:PW Q:vthp


I:PY(fe) Q:vhp(fe) fe.tl:

I:PCO2#(fe)$clim Q:hhco2(fe) P:1e-5 fe.tl:

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The “.tl” suffix instructs GAMS to

display each element of fe

Instructs GAMS to include a separate I:PCO2#(fe)

for each element of fe

• Similar expression are used to include emissions in other production functions

* Electricity production

$PROD:Y(i)$(vom(i) and ele(i)) s:0 kle:sigma("e_kl") va(kle):sigma("k_l")

+ ene(kle):sigma("fe") oil(ene):0 col(ene):0 gas(ene):0

O:PY(i) Q:vom(i)

I:PY(j)$(not fe(j)) Q:vfi(j,i)



I:PY(fe) Q:vfi(fe,i) fe.tl:

I:PCO2#(fe)$clim Q:fico2(fe,i) P:1e-5 fe.tl:

* Other output and refined oil production

$PROD:Y(i)$(vom(i) and not ele(i) and not ff(i)) s:0 kle(s):sigma("e_kl")

+ va(kle):sigma("k_l") e(kle):sigma("ele_fe") ne(e):sigma("fe")

+ oil(ne):0 col(ne):0 gas(ne):0

O:PY(i) Q:vom(i)

I:PY(j)$(not fe(j)) Q:vfi(j,i) e:$ele(j)



I:PY(fe) Q:vfi(fe,i) fe.tl:

I:PCO2#(fe)$clim Q:fico2(fe,i) P:1e-5 fe.tl:

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• Emissions allowances are endowed to the housel → revenue from the cap-and-trade program is returned to households

* Household demand

$DEMAND:HH

D:PW Q:vthp

E:PL Q:efh("lab")

E:PK Q:efh("cap")

E:PR(i) Q:vfm("res",i)

E:PCO2$clim Q:clim

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The quantity of emissions rights is controlled by clim

• The default level for all GAMS variables is 1. To replicate the benchmark dataset, we need to set the price of CO2 emission equal to zero.

PCO2.L = 0;

• ENERGY2 implements a 20% reduction in CO2 emissions

clim = 0.8*sum(i, fco2(i));

$include ENERGY2.gen

solve ENERGY2 using mcp;

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• Results reporting includes the quantity of emissions and the CO2 price

PARAMETER

EMISSIONS(*) CO2 emissions - million metric tons

PRICECO2(*) CO2 price $ per metric ton;

EMISSIONS("BASE") = sum(i, fco2(i));

EMISSIONS("SIM") = sum((fe,i)$vfi(fe,i),

fico2(fe,i)*FFE.L(fe,i)/vfi(fe,i))

+ sum(fe, hhco2(fe)*HFE.L(fe)/vhp(fe));

EMISSIONS("%C") = 100*(EMISSIONS("SIM")-EMISSIONS("BASE"))/EMISSIONS("BASE");

PRICECO2("SIM") = 1e3*PCO2.L/PW.L;

DISPLAY OUTPUT, WELFARE, EMISSIONS, PRICECO2;

EXECUTE_UNLOAD "ENERGY2_OUTPUT.gdx"

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Benchmark emissions of from fuel fe used in sector i

Ratio of fuel input fe used in sector i in

the simulation to that in the benchmark

• Results reporting includes the quantity of emissions and the CO2 price

PARAMETER

EMISSIONS(*) CO2 emissions - million metric tons

PRICECO2(*) CO2 price $ per metric ton;

EMISSIONS("BASE") = sum(i, fco2(i));

EMISSIONS("SIM") = sum((fe,i)$vfi(fe,i),

fico2(fe,i)*FFE.L(fe,i)/vfi(fe,i))

+ sum(fe, hhco2(fe)*HFE.L(fe)/vhp(fe));

EMISSIONS("%C") = 100*(EMISSIONS("SIM")-EMISSIONS("BASE"))/EMISSIONS("BASE");

PRICECO2("SIM") = 1e3*PCO2.L/PW.L;

DISPLAY OUTPUT, WELFARE, EMISSIONS, PRICECO2;

EXECUTE_UNLOAD "ENERGY2_OUTPUT.gdx"

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Economic data are in billions and

emissions data are in millions → multiply by (1e9/1e6)

Divide by a consumer price index so

that the numeraire choice does not influence the emissions price

All model output is sent to a gdx file

1. Implement a 30% reduction in emissions and analyze the results.

2. When there a 20% reduction in emissions, change the value of sigma("e_kl") from 0.5 to 1 and analyze changes in the CO2 price and welfare.

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Exercises

an introduction to energy-economic computable general

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